Data processing method for including the effect of the tortuosity on the acoustic behavior of a fluid in a porous medium

Abstract

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for processing data representing the effect of tortuosity on the acoustic behavior of a fluid in a porous medium. One of the methods includes generating by a first data processing program of the data processing apparatus, a model of acoustic behavior of a fluid in a porous medium including an effect of tortuosity, with the model comprising a time variable indicative of a sound speed of the fluid. The method includes rescaling the time variable of the model based on the sound speed in a fluid in the porous medium. The method also includes simulating the acoustic behavior including the effect of tortuosity of the porous medium based on the rescaling of the time-related variables within the model.

What is claimed is: 
     
       1. A method performed by a data processing apparatus for processing data representing the effect of tortuosity of a porous medium on the acoustic behavior of a fluid in the porous medium, the method comprising:
 receiving by a data processing program of the data processing apparatus, a time dependent model of acoustic behavior of the fluid in the porous medium, which time dependent model includes modeling an effect of tortuosity of the porous medium, with the model comprising a time variable indicative of a sound speed of the fluid in the porous medium; and 
 simulating the acoustic behavior including the effect of tortuosity of the porous medium based on the time variable. 
 
     
     
       2. The method of  claim 1  wherein the method further comprises:
 rescaling the time variable to account for the effect of tortuosity of the porous medium; and 
 determining acoustic behavior within the model including the effect of the tortuosity of the porous medium. 
 
     
     
       3. The method of  claim 2  wherein the acoustic behavior comprises dissipation and propagation of sound waves. 
     
     
       4. The method of  claim 2  wherein rescaling the time variable, comprises:
 adjusting the amount of time represented by one simulation time increment; and 
 rescaling at least one dynamic variable representing the porous medium in the model as a result of rescaling of the time variable. 
 
     
     
       5. The method of  claim 1  wherein simulating the acoustic behavior, further comprises:
 simulating fluid flow through or within a volumetric region including the porous medium. 
 
     
     
       6. The method of  claim 1  wherein the model includes a momentum sink that accounts for acoustic losses of the porous medium. 
     
     
       7. The method of  claim 2  wherein rescaling the time variable further comprises:
 rescaling the time variable based on nominal sound speed of the fluid and a sound speed of the fluid in the porous medium. 
 
     
     
       8. The method of  claim 1  wherein the fluid is represented by elements, and the elements have one or more properties of mass, density, momentum, pressure, velocity, temperature, energy, mass fluxes, momentum fluxes, and energy fluxes within the fluid. 
     
     
       9. The method of  claim 2  wherein rescaling the time variable adjusts the amount of time represented by one simulation time increment, and further comprises rescaling a temperature of the model. 
     
     
       10. The method of  claim 9  wherein rescaling the time variable further comprises rescaling a pressure of the model. 
     
     
       11. The method of  claim 9  wherein rescaling the time variable further comprises rescaling the velocity of the fluid. 
     
     
       12. The method of  claim 9  wherein rescaling the time variable further comprises rescaling the resistance of the porous medium. 
     
     
       13. A method performed by a data processing apparatus, the method comprising:
 processing by the data processing apparatus, data through a model of acoustic behavior of a fluid through a porous medium, which time dependent model includes modeling an effect of tortuosity on the acoustic behavior of the fluid in the porous medium; 
 rescaling by the data processing apparatus, a time variable of the model, with the time variable indicative of sound speed of the fluid, and with rescaling based on the sound speed in the fluid in the porous medium; and 
 simulating the acoustic behavior including the effect of tortuosity of the porous medium based on the rescaling of the time variable. 
 
     
     
       14. The method of  claim 13  further comprising:
 determining acoustic behavior within the model including the effect of the tortuosity of the porous medium. 
 
     
     
       15. The method of  claim 13  wherein the acoustic behavior comprises dissipation and propagation of sound waves. 
     
     
       16. The method of  claim 13  wherein rescaling the time variable further comprises:
 adjusting the amount of time that represents one simulation time increment resulting in rescaling at least one dynamic variable representing the porous medium in the model. 
 
     
     
       17. The method of  claim 13 , further comprising:
 simulating fluid flow through or within a volumetric region that includes the porous medium. 
 
     
     
       18. The method of  claim 13  wherein the model includes a momentum sink that accounts for acoustic losses of the porous medium. 
     
     
       19. The method of  claim 13  wherein rescaling the time variable further comprises:
 rescaling the time variable based on nominal sound speed of the fluid and a sound speed of the fluid in the porous medium. 
 
     
     
       20. The method of  claim 13  wherein the fluid is represented by elements, and the elements have one or more properties of mass, density, momentum, pressure, velocity, temperature, energy, mass fluxes, momentum fluxes, and energy fluxes within the fluid. 
     
     
       21. The method of  claim 13  wherein rescaling the time variable adjusts the amount of time represented by one simulation time increment, and rescaling, rescales one or more of a temperature of the model, a pressure of the model, velocity of the fluid and resistance of the porous medium. 
     
     
       22. A data processing apparatus comprises:
 a processor; 
 memory coupled to the processor; 
 a storage medium storing executable instructions for processing data representing an effect of tortuosity of a porous medium on acoustic behavior of a fluid in the porous medium, the instructions for causing the processor to: 
 receive a time dependent model of acoustic behavior of the fluid in the porous medium, which time dependent model includes modeling an effect of tortuosity of the porous medium, with the model comprising a time variable indicative of a sound speed of the fluid in the porous medium; and 
 simulate the acoustic behavior including the effect of tortuosity of the porous medium based on the time variable within the model. 
 
     
     
       23. The data processing apparatus of  claim 22  wherein the storage medium further comprises instructions to:
 rescale the time variable to account for the effect of tortuosity of the porous medium; and 
 determine acoustic behavior within the model including the effect of the tortuosity of the porous medium. 
 
     
     
       24. The data processing apparatus of  claim 22  wherein the acoustic behavior comprises dissipation and propagation of sound waves. 
     
     
       25. The data processing apparatus of  claim 22  wherein the storage medium further comprises instructions to:
 rescale a time variable, by adjusting the amount of time represented by one simulation time increment; and 
 rescale at least one dynamic variable representing the porous medium in the model as a result of rescaling of the time variable. 
 
     
     
       26. The data processing apparatus of  claim 22  wherein instructions to simulate the acoustic behavior comprise instructions to:
 simulate fluid flow through or within a volumetric region including the porous medium. 
 
     
     
       27. The data processing apparatus of  claim 22  wherein the model includes a momentum sink that accounts for acoustic losses of the porous medium. 
     
     
       28. The data processing apparatus of  claim 23  wherein instructions to rescale the time variable further comprises instructions to:
 rescale the time variable based on nominal sound speed of the fluid and a sound speed of the fluid in the porous medium. 
 
     
     
       29. The data processing apparatus of  claim 23  wherein the fluid is represented by elements, and the elements have one or more properties of mass, density, momentum, pressure, velocity, temperature, energy, mass fluxes, momentum fluxes, and energy fluxes within the fluid. 
     
     
       30. The method of  claim 23  wherein rescaling the time variable adjusts the amount of time represented by one simulation time increment, and further comprises or more of rescaling a temperature of the model, a pressure of the model, rescaling the velocity of the fluid and rescaling resistance of the porous medium. 
     
     
       31. A computer program product comprising executable computer instructions tangibly stored on a non-transitory computer readable medium, with the instructions including instructions for processing data representing an effect of tortuosity of a porous medium on acoustic behavior of a fluid in the porous medium, the instructions when executed causing a computing apparatus to:
 receive a time dependent model of acoustic behavior of the fluid in the porous medium, which model includes modeling an effect of tortuosity of the porous medium, with the time dependent model comprising a time variable indicative of a sound speed of the fluid in the porous medium; and 
 simulate the acoustic behavior including the effect of tortuosity of the porous medium based on the time variable within the model. 
 
     
     
       32. The computer program product of  claim 31  wherein the non-transitory computer readable medium further comprises instructions to:
 rescale the time variable to account for the effect of tortuosity of the porous medium; and 
 determine acoustic behavior within the model including the effect of the tortuosity of the porous medium. 
 
     
     
       33. The computer program product of  claim 31  wherein the acoustic behavior comprises dissipation and propagation of sound waves. 
     
     
       34. The computer program product of  claim 32  wherein the non-transitory computer readable medium, further comprises instructions to:
 rescale the time variable, by adjusting the amount of time represented by one simulation time increment; and 
 rescale at least one dynamic variable representing the porous medium in the model as a result of rescaling of the time variable. 
 
     
     
       35. The computer program product of  claim 31  wherein instructions to simulate the acoustic behavior comprise instructions to simulate fluid flow through or within a volumetric region including the porous medium. 
     
     
       36. The computer program product of  claim 31  wherein the model includes a momentum sink that accounts for acoustic losses of the porous medium. 
     
     
       37. The computer program product of  claim 32  wherein instructions to rescale the time variable further comprises instructions to:
 rescale the time variable based on nominal sound speed of the fluid and a sound speed of the fluid in the porous medium. 
 
     
     
       38. The computer program product of  claim 31  wherein the fluid is represented by elements, and the elements have one or more properties of mass, density, momentum, pressure, velocity, temperature, energy, mass fluxes, momentum fluxes, and energy fluxes within the fluid. 
     
     
       39. The computer program product of  claim 32  wherein instructions to rescale the time variable comprises instructions to:
 adjust the amount of time represented by one simulation time increment, and further comprises instructions to rescale a temperature of the model. 
 
     
     
       40. The computer program product of  claim 32  wherein instructions to rescale the time variable comprises instructions to:
 rescaling a pressure of the model. 
 
     
     
       41. The computer program product of  claim 32  wherein instructions to rescale the time variable comprises instructions to:
 rescale the velocity of the fluid. 
 
     
     
       42. The computer program product of  claim 32  wherein instructions to rescale the time variable comprises instructions to:
 rescale the resistance of the porous medium.